Non UBC
DSpace
Antonio Sa Barreto
2019-10-16T08:16:09Z
2019-04-18T08:46
We study the local propagation of singularities of solutions of $P(y,D) u= f(y,u),$ in $R^3,$ where $P(y,D)$ is a second order strictly hyperbolic operator and $f\in C^\infty.$ We choose a time function $t$ for $P(y,D)$ and assume that $f(y,u)$ is supported on $t>-1$ and that for $t<-2,$ $u$ is assumed to be the superposition of three conormal waves that intersect transversally at a point $q$ with $t(q)=0.$ We show that, provided the incoming waves are elliptic conormal distributions of appropriate type and $(\p_u^3 f)(q, u(q))\not=0,$ the nonlinear interaction will produce singularities on the light cone for $P$ over $q.$ Melrose and Ritter, and Bony, had independently shown that the solution $u$ is a Lagrangian distribution of an appropriate class associated with the light cone over $q$ and we show that under this non-degeneracy condition, $u$ is an elliptic Lagrangian distribution and we compute its principal part.
https://circle.library.ubc.ca/rest/handle/2429/71923?expand=metadata
40.0 minutes
video/mp4
Author affiliation: Purdue University
Banff (Alta.)
10.14288/1.0383404
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculty
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Global Analysis, Analysis On Manifolds, Dynamical Systems And Ergodic Theory, Global Analysis
Interaction of Semilinear Conormal Waves (joint work with Yiran Wang)
Moving Image
http://hdl.handle.net/2429/71923